Bài ôn tập chương VI

Home Lớp 11 Toán lớp 11 - Sách kết nối tri thức Bài ôn tập chương VI:Bài tập trung bình

{"common":{"save":0,"post_id":"7287","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5485","post_id":"7287","mon_id":"1158924","chapter_id":"1159168","question":"M\u1ed9t ng\u01b0\u1eddi g\u1eedi ti\u1ec1n ti\u1ebft ki\u1ec7m vào m\u1ed9t ngân hàng v\u1edbi lãi su\u1ea5t 7,2% \/n\u0103m v\u1edbi hình th\u1ee9c lãi kép. H\u1ecfi sau ít nh\u1ea5t bao nhiêu n\u0103m ng\u01b0\u1eddi \u0111ó thu \u0111\u01b0\u1ee3c s\u1ed1 ti\u1ec1n lãi ít nh\u1ea5t b\u1eb1ng s\u1ed1 ti\u1ec1n g\u1eedi ban \u0111\u1ea7u?<\/p>","options":["A.<\/strong> 10 n\u0103m","B.<\/strong> 11 n\u0103m","C.<\/strong> 12 n\u0103m","D.<\/strong> 13 n\u0103m"],"correct":"1","level":"2","hint":"","answer":"Ch\u1ecdn A.<\/strong> 10 n\u0103m<\/span><\/p>G\u1ecdi s\u1ed1 ti\u1ec1n ban \u0111\u1ea7u là P. S\u1ed1 ti\u1ec1n lãi nh\u1eadn \u0111\u01b0\u1ee3c sau n<\/strong><\/span> n\u0103m là $P(1+0,072)^n-P$<\/span>.<\/p>Ta c\u1ea7n tìm n<\/strong><\/span> nguyên d\u01b0\u01a1ng nh\u1ecf nh\u1ea5t \u0111\u1ec3 $P(1+0,072)^n-P \\ge P$<\/span> ⇔ $n \\ge \\log_{1,072}2\\approx 9,97$<\/span>.<\/p>V\u1eady n = 10<\/strong><\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 05:33:10","option_type":"txt","len":0},{"id":"5487","post_id":"7287","mon_id":"1158924","chapter_id":"1159168","question":"Có bao nhiêu s\u1ed1 th\u1ef1c d\u01b0\u01a1ng n khác 1 \u0111\u1ec3 $\\log_n81$<\/span> là m\u1ed9t s\u1ed1 nguyên?<\/p>","options":["A.<\/strong> 5","B.<\/strong> 3","C.<\/strong> 4","D.<\/strong> 6"],"correct":"4","level":"2","hint":"","answer":"Ch\u1ecdn D.<\/strong> 6<\/span><\/p>Ta có: $\\log_n81 = \\log_n3^4=4\\log_n3=\\dfrac{4}{\\log_3n}$<\/span>.<\/p>\u0110\u1ec3 $\\log_n81$<\/span> là m\u1ed9t s\u1ed1 nguyên thì $\\log_3n\\in \\{ \\pm1; \\pm2; \\pm4 \\}$<\/span> ⇔ $n\\in \\bigg\\{ \\dfrac{1}{3};3;\\dfrac{1}{9};9;\\dfrac{1}{81};81 \\bigg\\}$<\/span><\/p>V\u1eady có t\u1ea5t c\u1ea3 6 s\u1ed1 th\u1ef1c d\u01b0\u01a1ng n khác 1 th\u1ecfa mãn \u0111i\u1ec1u ki\u1ec7n bài toán.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 05:40:42","option_type":"txt","len":0},{"id":"5490","post_id":"7287","mon_id":"1158924","chapter_id":"1159168","question":"Ng\u01b0\u1eddi ta nuôi c\u1ea5y m\u1ed9t lo\u1ea1i vi khu\u1ea9n V trong phòng thí nghi\u1ec7m. N\u1ebfu s\u1ed1 vi khu\u1ea9n ban \u0111\u1ea7u là $N_0$<\/span><\/span> ,t\u1ec9 l\u1ec7 t\u0103ng tr\u01b0\u1edfng vi khu\u1ea9n là r<\/span> thì sau t gi\u1edd <\/span>s\u1ed1 vi khu\u1ea9n N(t) nuôi c\u1ea5y \u0111\u01b0\u1ee3c \u01b0\u1edbc tính theo công th\u1ee9c $N(t)=N_0.e^{rt}$<\/span>. Ban \u0111\u1ea7u có 300 con vi khu\u1ea9n và sau 4 gi\u1edd ng\u01b0\u1eddi ta th\u1ea5y s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n \u0111ã t\u0103ng g\u1ea5p \u0111ôi. S\u1ed1 gi\u1edd g\u1ea7n nh\u1ea5t \u0111\u1ec3 s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n thu \u0111\u01b0\u1ee3c là 9000 con là:<\/p>","options":["A.<\/strong> 19 gi\u1edd","B.<\/strong> 20 gi\u1edd","C.<\/strong> 22 gi\u1edd","D.<\/strong> 21 gi\u1edd"],"correct":"2","level":"2","hint":"","answer":"Ch\u1ecdn B.<\/strong> 20 gi\u1edd<\/span><\/p>Áp d\u1ee5ng công th\u1ee9c $N(t)=N_0.e^{rt}$<\/span> ta có:<\/p>600 = 300 . $e^{4r}$<\/span> ⇔ 4r = ln2 ⇔ r = $\\dfrac{\\ln 2}{4}$<\/span><\/p>\u0110\u1ec3 s\u1ed1 l\u01b0\u1ee3ng vi khu\u1ea9n thu \u0111\u01b0\u1ee3c là 9000 con thì:<\/p>300 . $e^{\\frac{ln2}{4}.t}$<\/span> = 9000 ⇔ $e^{\\frac{ln2}{4}.t}$<\/span> = 30 ⇔ $\\frac{ln2}{4}.t=\\ln30$<\/span> ⇔ t ≈ 19,628.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-07 05:51:20","option_type":"txt","len":0}]}